Question
Solve the inequality and represent the solution graphically on number line: 5 (2x – 7) – 3 (2x + 3) $\le$ 0 , 2x + 19 $\le$ 6x + 47.
✓
Answer
We have $5(2x - 7) - 3(2x + 3) \leqslant 0$ and $2x + 19 \leqslant 6x + 47$
$ \Rightarrow 10x - 35 - 6x - 9 \leqslant 0$ and $ - 4x \leqslant 28$
$ \Rightarrow 4x - 44 \leqslant 0$ and $x \geqslant - 7$
$ \Rightarrow 4x \leqslant 44$ and $x \geqslant - 7$
$ \Rightarrow x \leqslant 11$ and $x \geqslant - 7$
$ \Rightarrow 10x - 35 - 6x - 9 \leqslant 0$ and $ - 4x \leqslant 28$
$ \Rightarrow 4x - 44 \leqslant 0$ and $x \geqslant - 7$
$ \Rightarrow 4x \leqslant 44$ and $x \geqslant - 7$
$ \Rightarrow x \leqslant 11$ and $x \geqslant - 7$
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